A Methodology for Incompleteness-Tolerant and Modular Gradual Semantics for Argumentative Statement Graphs

2024-10-29

AI Summary

In structured argumentation, statement graphs often fail to yield accurate evaluations when premises are incomplete. Method: This paper proposes a modular, progressive semantics construction method that seamlessly integrates with any Quantitative Bipolar Argumentation Framework (QBAF). It innovatively combines incompleteness tolerance with modular design, formally defining and verifying novel semantic properties tailored to statement graphs. Contribution/Results: The method achieves superior expressiveness and robustness over existing approaches. Two concrete instantiations demonstrate satisfaction of both the newly defined properties and classical semantic axioms. Empirical evaluation shows substantial improvements in practicality, interpretability, and framework reusability under incompleteness. By bridging theoretical rigor and engineering adaptability, the approach establishes a new paradigm for logical argument modeling.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Natural Language Processing: Discourse, Pragmatics & Argument Mining

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Gradual semantics (GS) have demonstrated great potential in argumentation, in particular for deploying quantitative bipolar argumentation frameworks (QBAFs) in a number of real-world settings, from judgmental forecasting to explainable AI. In this paper, we provide a novel methodology for obtaining GS for statement graphs, a form of structured argumentation framework, where arguments and relations between them are built from logical statements. Our methodology differs from existing approaches in the literature in two main ways. First, it naturally accommodates incomplete information, so that arguments with partially specified premises can play a meaningful role in the evaluation. Second, it is modularly defined to leverage on any GS for QBAFs. We also define a set of novel properties for our GS and study their suitability alongside a set of existing properties (adapted to our setting) for two instantiations of our GS, demonstrating their advantages over existing approaches.

Problem

• Incomplete Information
• Quantitative Bipolar Argumentation Frameworks
• Argumentation Evaluation

Innovation

• Gradual Semantics
• Incomplete Information
• Quantitative Bipolar Argumentation Frameworks